Disgraced press baron Conrad Black received a boost in his quest for a release from prison today as US supreme court judges peppered prosecutors with sceptical questions over the controversial fraud law at the centre of his conviction.

Several of Black's family members including his daughter, Alana and his elder son, James, were in a packed public gallery at the highest court in America for a last-ditch appeal by the 65-year-old peer to overturn his six-and-a-half-year prison sentence for fraud and obstruction of justice. Black, who is incarcerated in Florida, was not allowed to attend.

The fallen media mogul's appeal lawyer, Miguel Estrada, told the nine supreme court justices that Black's conviction for embezzling from shareholders was unconstitutional because it depends on a contentious 28-word law that is "basically a mess", written with "vague, amorphous and open-ended" wording.

The law, originally drawn up to target corrupt public officials, allows for the conviction of people who deprive constituents, employers or shareholders of their entitlement to "honest services". It has been used in scores of high-profile cases including the conviction of the former Enron chief executive, Jeffrey Skilling, and an ongoing case against a former governor of Illinois, Rod Blagojevich, who has been accused of trying to "sell" president Barack Obama's former senate seat.

Several of the judges clearly indicated unease with the law, repeatedly interrupting the deputy US solicitor general, Michael Dreeben, who was arguing that Black's convictions should stand.

One of the court's more liberal judges, Stephen Breyer, wondered whether it was so broadly drawn that it could be used to prosecute somebody who uses working hours to read horse-racing form in a newspaper. He suggested that under a loose interpretation, the law could "criminalise" millions of people. "There are 150 million workers in the United States," Breyer told Dreeben. "I think possibly 140 million would flunk your test."

Once the head of a global media empire who counted Baroness Thatcher, Princess Michael of Kent and Henry Kissinger among his friends, Black was found guilty by a Chicago jury in 2007 of plundering $6.1m from shareholders in his Hollinger newspaper company, which owned 200 titles at the height of its fortunes including the Daily Telegraph, the Chicago Sun-Times and the Jerusalem Post. Since entering jail in early 2008, he has been helping inmates with their literacy.

The peer, who has been stripped of the Conservative whip in the House of Lords, failed to overturn his convictions through an initial appeal. But his legal team scored a major coup by persuading the supreme court to grant an oral hearing‚ a privilege only afforded to roughly 100 out of 10,000 petitioners annually.

The hearing was held with considerable ceremony in a room surrounded by red velvet curtains, marble columns and ornate stone friezes. One of the supreme court's judges, Antonin Scalia, has repeatedly expressed unease about the "honest services" statute used in the case, suggesting earlier this year that it invites "abuse" by headline-grabbing prosecutors targeting "any manner of unappealing or ethically questionable conduct" rather than out-and-out fraud.

Emerging from court, one of Black's team of defence lawyers suggested that eight out of the nine justices appeared worried about the law's validity. The supreme court is due to hear an appeal by Enron's former boss on similar grounds next year and is likely to rule on the issue by June. If the judges decided that the statute needs amendment, Black's convictions could be overturned or referred back to lower courts for re-examination.